It is possible that the oil pump is bad. Hopefully not, but a possibility.
First thing that I would do is a full oil/filter change, regardless of when it was last done. Also use a good quality oil filter (Wix is popular) to ensure that is not the issue.
I wouldn't go a heavier oil yet, as that may mask the underlying problem, which could be as simple as a faulty oil pressure sender.
If you have access to a test oil pressure gauge (preferably mechanical) that is a great way to test the actuall pressure and help diagnose the OEM sender.
Start with the basics, oil filter change, and proceed from there.
Keep us posted as to what you have done and the results.